Question

Complete the input-output table for log4X. How would I solve this?

Answer 1

Answer:

$x \to f(x)$

$0.25 \to -1$

$0.5 \to -0.5$

$1 \to 0$

$2 \to 0.5$

$4 \to 1$

$8 \to 1.5$

Step-by-step explanation:

Given

$f(x) = log_4(x)$

$x = 0.5$

$f(x) = log_4(x)$

$f(0.5) = log_4(0.5)$

Apply law of logarithm

$f(0.5) = \frac{log(0.5)}{log(4)}$

Using a calculator, we have:

$f(0.5) = -0.5$

$x = 1$

$f(x) = log_4(x)$

$f(1) = log_4(1)$

Express 1 as 4^0

$f(1) = log_4(4^0)$

Apply law of logarithm

$f(1) = 0*log_4(4)$

$f(1) = 0$

$x = 2$

$f(x) = log_4(x)$

$f(2) = log_4(2)$

Apply law of logarithm

$f(2) = \frac{log(2)}{log(4)}$

Using a calculator, we have:

$f(2) = 0.5$

$x = 4$

$f(x) = log_4(x)$

$f(4) = log_4(4)$

$log_a(a) = 1$

So:

$f(4) = 1$

$x = 8$

$f(x) = log_4(x)$

$f(8) = log_4(8)$

Apply law of logarithm

$f(8) = \frac{log(8)}{log(4)}$

Using a calculator, we have:

$f(8) = 1.5$

So, the complete table is:

$x \to f(x)$

$0.25 \to -1$

$0.5 \to -0.5$

$1 \to 0$

$2 \to 0.5$

$4 \to 1$

$8 \to 1.5$